"Network Emergence: How Small Worlds Make a Big Difference in the Broadway Musical Industry, 1877 to 1995", Brian Uzzi, February 14, 2003
Strategy seminar, University of Toronto Rotman School, Friday, February 14, 2003, 1:00 pm
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Welcome by Kim Bates, Rotman School
What are they putting in the water in Long Island?
Brian Uzzi, Northwestern University
Work with Jarrett Spiro (Northwestern University), and Dimitri Delis (Northwestern Unviersity & Delis Investment Incorporated)
New work on the small world problem
Small worlds have captured the attention of physicists, sociologists, ...
Across disciplines, small worlds pop up in areas diverse from each other.
Power grid, brains of worms, actors, ...
Small worlds feature a network both highly clustered, but with short pathways
Most networks have long pathways, because people live in clusters
Something fundamental, in the way things get organized.
What accounts for the process in which small worlds form?
Do small worlds actually make a difference?
Does it make the system work better or worse, or doesn't it make a difference.
Some research in the Broadway musical industry
Network of creative artists
Starting in 1877 "The Black Crook", to 1995
How do networks emerge? What process?
How do they impact the success? How well in box office? How well in artistic success?
A small world develops quickly in the early times of the industry.
First 20 years, lots of randomness.
Then over 5 years, a small world structure emerges.
Then the small world persists over the next 100 years -- over World Wars, entrance and exit of lots of creative networks.
Then, will show the impact on the artists and commercial development of the industry
Interest in the overall structure, the global network, not just the individual
Small worlds vary in their small worldliness, which impacts what happens in the system
What leads to these questions?
The small world idea from the study by Stanley Milgrom, 1967
Milgrom had two passions: work and travel.
Would travel to Madagascar.
Discovered that he knew people through other people, ending the conversation with "isn't it a small world"?
Opens phone book, picks a stockbroker at random.
Sent to 160 people across the U.S.
Instructions to forward the note to stockbroker, or someone closer
Discovered that people are separated by six degrees of separation
Short separations were unusual.
Milgrom extrapolates from the data -- which was very dirty -- with genius.
The reason that worlds are so short, is because people live in clusters.
But there are a few people that connect these clusters.
Then don't have to go through all of the networks.
Discovered 60% of people pass through the same four people
Two of these people were travelling salesmen
1970, Granovetter is in the same department as Milgrom in Harvard
Takes the research an extra step.
The cluster is where people share common ideas and knowledge.
Interested in the bridges bringing clusters together.
The strength of weak ties
1977, Ron Burt builds on Granovetter with structural holes
Finds structures are quite stable over a 30 year period, don't change.
1997, Duncan Watts
Comes up with quantitative measures of small worlds.
Back to Milgram, comparing to random networks
Also develops a bipartite random network.
When people enter a network, they don't enter as an individual, but as a cluster of people, all working together.
People tend to enter worlds already clustered.
Makes worlds look more clustered than they are.
This inflation was removed by Watts.
The difference can be seen when compared to random networks.
Emergence: How does networks form?
Global network behaviour: Do they make a difference?
Qualitative visual analysis (for small networks)
Works well when network is early, because network is sparse.
Software package, Pajek, from Sante Fe Institute, where he was a visiting fellow last year
Quantitative analysis (for large networks)
Rate of emergence is quite rapid
Robustness of network structure of time
Impact of global network structure over time
Building on Watts and Milgrom
If a small world is inevitable, it's not worth studying, so what else could it be?
What are the alternative ideal structures
As people start to work together, they work in clusters they started with, and don't work with anyone else.
e.g. rock musicians always work with the same people.
Clusters become linearly connected
This is a weak network structure.
Can fall apart easily if any connecting nodes break off
Path lengths are very long, where people need to go through many links.
Could have overlapping connections
Multiple shortcuts to bring togheter
Everyone connects to everyone else -- Ehromer
Rock musicians who work with everyone else
What do we find, in the Broadway music industry?
From vaudeville, burlesque and opera, to create something new
Vaudeville: lots of short skits tied together, not related to anything
Short stumpy guy, then a woman with a goat, then a juggler.
The next night, a different act.
Burlesque, peak in 1920s with Gypsy Rose Lee
One step up: large productions, lavish, combine music and social protest
More stability: shows would pretty well be the same.
Still, not connected stories.
Same characters, every show
Music and dance are fixed together
Called "musical opera" first, Broadway musicals came from these three areas
An influx of new people, getting off a boat from Europe
Almost all musicals are created by six specialists, as compared to hundreds of people in a movie.
Producer, connected to financiers
1890 Ol' Nelly connected to 1891 Black Velvet, through Harry B. Smith
Ties are that they work collaboratively, to build the musical.
The tie remains in the data for 7 years, and is then removed unless the people work together again.
At 5 to 7 to 10 years, pretty good confidence interval for people not working together again in statistical analysis.
Previous research on emergence leaves all of the ties in, which distorts results, e.g. people from 1900 tied to 1970s
Pie charts: Divide central and periphery creative artists
Do people show up more often? e.g. more producers in the core rather than librettists?
No, not significant, low chi-squared.
Creative artists don't include performers
Extremely well documented by afficianados
Description of production
Members of the creative team
Measures of success
Number of performances, including shows that died in pre-production
Financial outcomes: hit, flop or failure
Critical reactions: rave to pan, 7 point scale
[Question about broader networks in other theatre centers?]
Defining as the network of people that work on Broadway productions
People working on vaudeville are considered a different type of network
Baudman: once people who made the jump to Broadway musicals, didn't do Broadway
Will see where a number of people are lost to Hollywood, but define the Broadway network to exclude that.
[Comment: Broadway becomes a provider to other theatre centres: touring companies?]
Distinction between an original production, a revival and a road show.
We look only at original productions.
1878 to 1995 [graphs]
Number of new musicals slow until 1890s, then drop around 1919 for war, then around WWII
Visual analysis focuses on the early period
Quantitative analysis works on the larger scale
Pajek -- network visualization program
If Joel and I have worked together in the past, then it will draw us closer together.
If three of use work together, it will draw us even closer together.
Black nodes for incumbents, white nodes for new entrants
In 1893, year 16
30 artists continuing, 6 new people
Overall chart very spread out -- a very fragmented network.
In 1894, year 17
36 continuing artists, 31 new artists -- European Jews who can read and write, who join the industry
Networks held together by Max Freeman, Harry B. Smith, and Reginald de Koven
Some networks are isolated
Preferential attachment: important
Networks grow as new people attach to an existing network
People who have a lot of attachments get even more.
In 1895, year 18:
Another boatload of immigrants.
The braided structures start to grow.
A large proportion link together.
Two full braided structures, not connected.
It would only take one link to tie them together.
Charles Frohman didn't get along with the other people, particularly Max Freeman
In 1896, 135 continuing with 29 new
See the beginning of a small world
Two braided structures begin to form a ring.
The path lengths have shrunk a great deal from the previous years.
The paths are multiple, through multiple people
Preferential attachments continuing.
A large independent cluster, which never gets anyone else to attach, and then leaves the network
In 1897, develops a real small world, with clustering and short paths
More preferential attachments
A lot of dots on top of each other
Increased preferential attachment
In a series
From fragmentation ...
... to braids ...
... into a ring ...
... which becomes a small network.
[Question: Does the network ever become fully connected?]
Emergence: braids turning into a ring happens very quickly.
The reason a small world obtains, is the result of two factors:
There's a few people who connect people together
The fit get fitter
The periphery is highly clustered.
The core is not clustered tightly, but have short pathways.
Finding: the periphery is very important
Creativity and new ideas from the periphery.
The core / periphery balance is very important
[Question: Can you explain all of these through demographics, rather than by structure?]
A patterned demographic process?
When someone new makes it, they make it in the unconnected part of the graph, and then joint the bigger cluster.
Yes, have done this when looking at the star industry model
People who get to the core don't stay there, by outperforming.
Jerome Kern, had lots of flops, but stayed in the core
More randomness in the graph structure, depending on how much entry and exit.
Preferential attachment: key paradox against high clustering.
This keeps the small world a small world
What about the rest of the industry?
From Watts: look at the cluster coefficient of the rest of the network, and compare it to the random network of the same size.
Actual / random should be 1, or orders of magnitude larger
Cluster coefficient, (CC) need to remove the bias of people just entering the network
Newman, Watts and Stogatz
Path length (LL) remains just about 1, conforming to short paths
Consistent over time
Actual to random: not a small world at first, then grows to 1920s, then drops off.
From a few hundred players to thousands, at the end
Red line is the actual cluster coefficient
See that the actually CC is much greater than the random CC
CC = .75 means that 75% of people can be connected to each other.
CC = .50 means that can explain with a random model.
The network becomes much more clustered, and less random
In 1929, introduction of talkies draws away a huge number of artists, as well as the consumer base.
This creates uncertainties in the network -- more can be explained by randomness
There are no exact statistics test, i.e. at one point, this is not a small world and at another this is -- it's only comparative
At about 200 nodes, turns into a small world
It's a bipartite network
In a unipartite network, would see a change in the order of magnitude.
As next step, (after seeing the emergence of the network), what difference does the small world have on the output?
Compare to randomness.
When lots of order in the system, get back to Granovetter.
It's good for people to have friends, to create a cradle for innovation.
However, if there's too much order and clustering, then people aren't getting signals from the outside world.
Would like new and novel ideas to come in.
Coming in through random networks, couldn't predict that these people would want to come into the network.
Want to bring in people with ideas.
If you don't know in advance, how do you know who to bring in? It's a creative industry.
Argue that random ties into the network do this.
Quote from Harold Prince, about Jerome Robbins.
Learned to look at musical theatre form ... investing .... Not dependent on dance, ... open to many influences, .... Serious subject matter.
Related to random, on the musical Caberet from Harold Prince, which had a lot of innovation. Fred and John, outside the Broadway musical industry, and written songs but no characters.
Actually had two shows. The book, and Prince's 15 minutes. Fred and John put them into scenes ... connected higgly-piggly throughout the scenes, but then put the two shows together.
Worked on Caberet from Harold Prince.
[A long and involved discussion happened about the comparison with "random"]
Dependent variables hit vs. flop vs. failiure; and pan to rave review
Independent variables ...
If too much randomness, bad; if not enough randomness, also bad.
Do find this U-shaped relationship.
Ordered probit model.
Model are best at predicting flops
Do best in the middle, increases probability of success 150% if stay in the middle.
Order is REALLY bad for artistic success
Could be critics saying it's the same old thing.
(Some self-selection, as pre-production failures aren't included)
Emergence happens rapidly.
Stability after emergence
Small world isn't binary, it's continuous
Amount of order and randomness in system, which impacts the system.
Can't have too much randomness, and can't have too much order.,